Which trigonometric function is represented by y = sin x?

The function represented by ( y = \sin x ) is indeed the sine function. The sine function describes the ratio of the length of the opposite side to the hypotenuse of a right triangle for a given angle. It is a fundamental trigonometric function that oscillates between -1 and 1 as ( x ) varies, typically measured in radians or degrees.

In the context of the unit circle, the sine of an angle corresponds to the y-coordinate of a point on the circumference of the circle. This makes the sine function particularly important in many areas of mathematics, physics, and engineering, as it relates to waveforms and oscillatory motion.

The other functions mentioned—tangent, cosine, and secant—are distinct from the sine function. The cosine function, for example, refers to the ratio of the length of the adjacent side to the hypotenuse, while the tangent function is the ratio of sine to cosine. Secant, on the other hand, is the reciprocal of cosine. Each serves its unique purpose in trigonometric calculations, but ( y = \sin x ) specifically indicates the sine function.